O(n) alternative to Quantum Fourier Transform with efficient neural net classical post-processing

arXiv:2605.16998 · quant-ph, cs.LG · Submitted 2026-05-16 · Read on arXiv

quant-ph, cs.LG

Submitted: 2026-05-16

Updated: 2026-09-15

Comments: Added evidence for efficient scaling of neural-network decoding; strengthened the numerical support through full Shor factoring simulations at larger system sizes; and improved the presentation for clarity and accessibility

Code: https://github.com/Fragecity/altqft

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Fisher Information — 14× in this paper · explained in 3 episodes
• Accuracy — 10× in this paper · explained in 1 episode
• Hidden Subgroup Problem — 10× in this paper
• Benchmark — 8× in this paper · explained in 2 episodes
• Quantum Fourier Transform — 7× in this paper
• Sample Complexity — 4× in this paper · explained in 15 episodes
• Fidelity — 3× in this paper · explained in 2 episodes
• Robustness — 3× in this paper · explained in 5 episodes
• Score Function — 3× in this paper · explained in 4 episodes
• Quantum Circuits — 2× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Quantum measurements and the Abelian Stabilizer Problem
• The Hidden Subgroup Problem - Review and Open Problems
• Demonstrating Record Fidelity for the Quantum Fourier Transform
• An approximate Fourier transform useful in quantum factoring
• Quantum Fourier Transform using Dynamic Circuits
• Towards a Neural Statistician
• Learning Hamiltonians for $O(1)$ Oracle-Query Quantum State Preparation

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